A commuter must pass through three traffic lights on the way to work. For each light, the probability that it is green upon arrival is 0.6. The lights are independent.

a. What is the probability that all three lights are green?

b. The commuter goes to work five days per week. Let \(X\) be the number of times out of the five days in a given week that all three lights are green. Assume the days are independent of one another. What is the distribution of \(X\) ?

c. Find \(P(X=3)\).